Q33E If the matrix [abcdefghi] is inv... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 2: Q33E (page 108)

If the matrix $[\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}]$ is invertible, then the matrix $[\begin{matrix} a & b \\ d & e \end{matrix}]$ must be invertible as well.

Short Answer

Expert verified

The statement is false.

Step by step solution

Objective

The given statement is 鈥渋f the matrix $[\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}]$ is invertible, then the matrix $[\begin{matrix} a & b \\ d & e \end{matrix}]$ is invertible.鈥� The objective is to determine whether or not the given statement is true.

Result

Consider the matrix $A = [\begin{matrix} 1 & 2 & 3 \\ 1 & 2 & 4 \\ 6 & 7 & 8 \end{matrix}]$ . det(A) = 5 Therefore, A is invertible.

Let $C = [\begin{matrix} 1 & 2 \\ 1 & 2 \end{matrix}]$

det(C)=0

Therefore, C is not invertible.

The matrix $[\begin{matrix} 1 & 2 & 3 \\ 1 & 2 & 4 \\ 6 & 7 & 8 \end{matrix}]$ is invertible but the matrix $[\begin{matrix} 1 & 2 \\ 1 & 2 \end{matrix}]$ is not invertible. Therefore, the given statement is false.

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91影视

If the matrix $[\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}]$ is invertible, then the matrix $[\begin{matrix} a & b \\ d & e \end{matrix}]$ must be invertible as well.

Short Answer

Step by step solution

Objective

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91影视

If the matrix [abcdefghi] is invertible, then the matrix [abde] must be invertible as well.

Short Answer

Step by step solution

Objective

Result

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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

If the matrix $[\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}]$ is invertible, then the matrix $[\begin{matrix} a & b \\ d & e \end{matrix}]$ must be invertible as well.